Computing circuits



o. L. PATTERSON 2,978,178

April 4, 1961 COMPUTING cmcurrs Original Filed Jan. 13, 1954 LKI4 3Sheets-Sheet 1 l2 1 v 2 RI 22 ,5 =1" a F l G.

R5 R+R3 f (A) E RE I R+R, (B)

RE m (I E2 R +2 RE (2) R +l (3) R E2 INVENTOR.

.5 OMAR PATTERSON I 0 LEE- E 1": "I g 4 ATTORNEYS April 4, 1961 o. L.PATTERSON 3 Sheets-Sheet 2 ADDING l A A cmcun 140 [I44 ADDING 2'46MULTIPLYING 6 e clncun' GIRGUIT [I42 ADDING E E CIRCUIT E2=EB 88 E B TADDING P ge F cmcun I L (E e E e +e e (9) E (E +e )(E +e EA a (IO) E,.=F(E, e e +e e K F I G 3.

INVENTOR.

OMAR L. PATTERSON ATTORNEYS April 1961 o. L. PATTERSON 2,978,178

COMPUTING CIRCUITS Original Filed Jan. 13, 1954 3 Sheets-Sheet 3 LIMITEDRANGE MULTIPLIER E, E, I 1-: /l88 x so e 5 I00 I00 2 5X50 E] 'l-I5O)IE2+I5O) '92 HIGH GAIN 5 E. E2 DIFFERENTIAL E= loo AMPLIFIER 5o E' 5g 40 5 50 I98 E +E +e fi- (a, |50)(E2+I50) 200 SR l E2 0 Fi INVENTOR.OMAR L. PATTERSON ATTOR NEYS COMPUTING CIRCUITS Omar L. Patterson,Media, PaJ, assignor to Sun Oil Com pany, Philadelphia, ;Pa., acorporation of New Jersey Original application'Jan. 13,1954, Ser. No.403,799.

Divided and this application Sept. 16, 1957, ,Ser. No- "684,630 a I4Claims. Jl. 2 l35 1 93)' Thisinvention relates to computing circuitsand, particularly, to circuits for the performance of multiplicationand/or division. r

This application is a division of my application Serial Number 403,799,filed January 13, 1954.

Since the process of multiplication is non-linear, it presents a verydifficult problem in electrical computing apparatus wherea high degreeof accuracy and response time are required. Multiplication has beenaccomplished by electromechanical devices, carrier waveform systems,non-linear elements, multivariable tube characteristics, and variousmodulation systems. Electromechanical devices and carrier systems arecapable of providing accuracies of the order of 0.l percent but havepoor response time. volving non-linear elements and characteristics aregenerally restricted to a range of 1 to percent in accuracy but arecapable of a high speed of response.

The present invention relates to circuits for the performance ofmultiplication and/o1- division which combine high accuracy and goodfrequency response. As'

will become clear hereafter, the invention relates to what might bereferred to as parametric multiplication and division, involving theintroduction of a dependent parameter which is mathematically eliminatedfrom a pair of equations to secure multiplication and/or division.

7 The general object of the invention as well as detailed objectsparticularly relating to features of construction and operation'willbecome apparent from the following description read in conjunction withthe accompanying drawings, in which:

- Figure 1 is a wiring diagram illustrating one embodiment of theinvention utilized for the carrying out of multiplying or dividingcomputations;

Figure 2 comprises curves illustrating the'operation of the circuit ofFigure land also embodies certain equations pertinent thereto;

Figure 3 comprises a block diagram and various equations pertinentthereto, the diagram illustrating the fashion in which negative as wellas positive quantities may be multiplied or divided; and

Figure 4 is a diagram and various expressions pertinent theretoillustrating a further fashion in which negative as well as positivequantities may be multiplied.

Reference may be made first to Figure 1 which shows,

a circuit capable of producing high accuracy results with rapidresponse. With a resolution time of ten microseconds an accuracy ofabout 1% may be obtained with this circuit while an accuracy of.0.l% maybe obtained with a resolution of 100 microseconds.

j ln'put potentials which are to'be multiplied together and areindicatedas E 'and E are applied, respectively,

at terminals 2 and.4. A potential input E is applied at.

terminal 6 and represents a quantity by which the product of E and E maybe divided. In the case of multiplication alone, E may be a constant andwill appear as a constant of proportionality. On the other hand, ifdiviqe i rYel edt 519K132. u,.be 2 m s and if new On the other hand,systems in-' a reciprocal of E is desired, both may be constant. The

circuit and is described on page 343 of volume 19, Waveparticularfashion in which the potentials are applied may vary with therequirements. For high speed operation, low impedance sources aredesirable and these maybe provided through the use of cathode followersor. other devices The input. signals themselves may have variousorigins, ranging from constant or slowly varying sources to sourcesinvolving rapid changes including,.for example, the sampling ofwaveforms at particular instants as described in my application SerialNo.

296,583, filed July 1, 1952. .As will appear from what follows, thecomputation is .completed in the circuit in each of a number of repeatedcycles of operation and it need only be assumed that the inputpotentials are constant over the duration of a single period. If theinputs are waveforms having a common cycle of repetition, which cyclehas a period which is long in comparison with the cycles of the presentcircuit, the product and/or quotient may be emitted as a waveform havingthe same repetition cycle as the inputs. It will become apparent,

however, that the computing circuit is of very wide: applicability tonumerous types of computers and will.

give an output corresponding to what may be regarded as a steady stateexisting only for the duration of one of' the repetition cycles of thecircuit.

The terminals 2 and 6 are respectively connected through resistances 8and 10 to the anodes of a pair of. diodes 12 and 14,' the cathodes ofwhich are joined at 1 16 and connected through resistance 18 to aconstant.

negative potential terminal 20. The anodes of the diodes 12 and 14 areconnected through diodes 22 and 24, having polarities as indicated, tothe ungrounded terminals of a pair of condensers 26 and 28 which aregrounded at 30. The ungrounded terminals designated 25 and 27 areconnected to resistors 32 and 34 in series with which there is located apotentiometer 36 the contact of which is grounded. As will becomeapparent hereafter, accuracy of operation depends upon the identity ofthe time constants of the two RC circuits involving the.

condensers 26 and 28, the resistors 32 and 34, and the resistance ofpotentiometer 36. Designating the capaci-.

ties of the condensers 26 and 28 as C, and the resistances betweenterminal 25 and the potentiometer contact, and between terminal 27 andthe potentiometer contact as R, the product RC must be maintainedconstant. For this purpose, it is desirable that the two RC circuitsshould be located in close proximity in a common housing to minimize theeffects of temperature variations, with the two circuits employingelements having identical temperature coefficients. Any residualdifferences may be cancelled out by adjustment of the contact ofpotentiometer36 or by providing fine adjustment of the capaci ties ofthe condensers 26 and 28. It may be remarked,

as will appear hereafter, that the low reverse conductances of thediodes may play aminor part in the operation and the adjustment of thepotentiometer may take .these into account. In any event, the twocircuits may be adjusted to secure very accurate correspondence of thetime constants.

Employed in the circuit is a simple and accurate amplitude comparisoncircuit which is known as a multiar forms, 'of the Radiation LaboratorySeries. The terminal 27 is connected at 38 to the secondary of atransformer 40 and through it to the cathode of a diode 42 which isconnected through condenser 46 to the grid of 1 I a pentode 48constituting the multiar tube.

$9 $99. thmash .t e tin au 9 .1 12 ransform r .49.

Patented Apr. 4, 1961 in, a cathode follower arrangement returningto afixed. The cathode of triode 56'is connected to the cathode of a diode58 the anodeof which negative potential terminal.

is connected to the ungrounded terminal of a condenser 60 andalso to thegrid of a triode 62 alsoarranged in. a cathode follower circuitreturned. to thenegative potential source. The output is taken from thecathode of triode 62 through terminal 64.

The diodes illustrated in the circuit may be either of vacuum or crystaltype.

The operation may be best described by assuming, as will be justifiedlater, that the multiar circuit has effected a charging of condensers 26and 28 by the delivery of a positive pulse through condenser 52 and thatthe multiar pentode 48 is, at the beginning of operation, highlyconducting, with the result that at terminal 16 there is no output fromthe multiar which disturbs the.

existence of a negative potential at the terminal 16 resulting fromcurrent fiow from terminal 6 through resistor 10, diode 14 and resistor18, andvfrom terminal 2 through resistor 8, diode 12 and resistor 18.Under these conditions, the anodes of diodes 22 and 24 will be atnegative potentials lower than any occurring during.

operation about to be described so that the diodes .22

and 24 are cut off. Prior to this, the multiar will have produced'apositive pulse at terminal 16 sufficient to effect cut-off of the diodes12 and 14 so that charging of, condensers 26 and 28 will have takenplace respectively through resistances 8 and 10, with the result thatthe respective condensers will have been charged to potentials given bythe expressions at the upper portions of the curves (B) and (A) inFigure 2, respectively. The resistances of resistors 8 and 10 aredesignated R and R respectively. The time t may be considered theinstant at which, following the charging just referred to, the diodes 22and 24 are cut off.

The condensers 26 and 28 now discharge through the resistors 32 and 34exponentially in accordance with the right-hand expressions in Equationsland 2, t being the, These discharges are indicated graphically in.

variable. the curves (A) and '(B). The discharge continues until thepotential of condenser 28 at terminal 27 reaches the value E introducedat terminal 4. At the instant this equality is reached, the diode 42begins to conduct to start to drive the control grid of pentode 48negative, this control grid having theretofore been connected to the.positive potential supply line through resistor 50. The action isregenerative, through the feedback afforded through transformer 40, andthe pentode 48 is sharply cut off. A steep positive pulse is thusdelivered through condenser 52 to terminal 16, cutting oif diodes 12 and14 and thus rendering conductive diodes 22 and 24 to initiate rechargingof the condensers 26 and 28. This action occurs at the instant t Duringthe drop of potential of terminal 25 of condenser 26, the potential E ofthis terminal follows the exponential law givenin Equation 2 of Figure 2until the time t, at which the pentode 48 is cut off. Noting that theexponential functions in Equations land 2 both have the identical value,it follows that E has-at thisinstant the value given by the Equation 3,representing the prod-, not of B by E divided by E, and multiplied bya-constant depending upon the resistances, which constant is unity if Requals R As pointed out above, the .RC product must be the same for thetwo condenser discharge circuits, including the back resistance of thediodes. Adjustment for such constant value of the time constantisjprovided by the adjustment of potentiometer 36.

The potential Egat-thegridoftriode56 givesa cor responding potential atits cathode and current flows through the diode 58' to bring thecondenser 60 to a' indicated inFigure 2-. which is determined by thegrid. -time' constant consisting of the product of the value of thecapacity at 46 multiplied by the sum of the resistances at 50 and 54.This time constant is so chosen as to make t more than sufficient toallow complete recharge of the condensers 26 and 28. Since the positivepulse resulting from cut off of pentode 48 rises very rapidly, asindicated in curve (c) of Figure 2, the, condensers 26 and 28 startrecharging almost immediately after, theinstant t This cuts offconduction through diode 42 and because of this action the usual troubleof bouncing? which is experienced with multiar circuits is notencountered. With the initiation of recharging, the diodeSS is cut offso that the condenser 60 retains the charge which it received during thecondenser discharge previously described. The demodulator, therefore,acts as a negative, peakvoltmeter, and the condenser60 will be fullycharged in a single cycle if triode 56 is arranged soas to beheavil'yconductive. The multiar recovers in the usualfashion, with a drop of itsanode potential to a low value characteristic of heavy conduction of thepentode. The recovery time of the multiar is the main andthere wasaccordingly stressed the maintenance of equality of the time constantsof the two condenser dis.- charge circuits. However, if the timeconstants are unequal a more general result may be securedas'expressedby Equation 4 in which K'isa constant, R C is the time'constant of the circuit of condenser 28, and R C is the time constant ofthe circuit of condenser 26. As will be evident from this equationpowers of inputs other than unity may be involved and, specifically, byequating of E, with either E or E (the other being constant), E willappear as any of a wide range of powers of E. If E is a function of timeslowly varying with respect to the periods of the repetition cycle apower function may be developed as a step function smoothable byfiltering.

.Power functions may be thus far more accurately produced than byhitherto known methods.

The circuit of Figure 1 involves the same limitation as other knownmultiplying circuits of being unable to multiply directly negativequantities to give proper signs of outputs. However, this difficulty isreadily overcome in accordance with what is diagrammed in Figure 3,involving association with the multiplying circuit of variousaddingcircuits.

Assuming that it is desired to multiply quantities represented bypotentialsE and'E which may have either positive or negative values,with the result of securing properly signed products, the potential E isadded in a-conventional adding circuit to a fixed positive potential ewhich is of such magnitude that the sum will always be positive. Thepotential B is likewise added in acircuit 142 to a fixed potential 2havingthe same property of producing a sum outputwhich .will always bepositive." These'two'positive'quantitiesare then intro- It will beevident from what has been described duced into the multiplying circuit144 which may be of the type shown in Figure 1 or, in fact, of'manyother types. The product E, from the multiplying circuit will then havethe form indicated in Equation 9 in which K is a constant. A furtheradding circuit 146 is provided which not only has the inputs E and E butan input corresponding to the product of e and e;;. It should be notedthat these last quantities are constants and, accordingly, thislastintroduction amounts only to the introduction of a fixed potential. Inthe adding circuit 146, by means of suitable resistances andpotentiometers, the inputs are added to provide an output which isindicated in the diagram. It should here again be noted tl It e and e;;are merely constants and, therefore, represent mere proportions of theinputs E and E The output from the adding circuit 146 is fed to anadding circuit 148 where it is added to E, from the output of themultiplying circuit. The output of circuit 148 designated E is as givenin Equation 10 from which it will be noted that it is proportional tothe product of E and E The adding circuits may be of any wellknowntypes, the term adding being here used to include subtraction. Forexample, highly precise circuits of this type are disclosed in myapplication Serial No. 239,279, filed July 30, 1951, now Patent No.2,855,145, issued October 7, 1958. It will be evident that followingthis procedure the multiplication of negative quantities will result inproducts of proper sign.

Another circuit for extending the range of multiplication to that ofnegative quantities is illustrated in Figure 4 and involves the use of ahigh gain diiferential amplifier. In explanation of the operation thereare indicated in Figure 4 potentials appearing at various points of thecircuit, and for purposes of illustration it is assumed that the inputpotentials to be multiplied vary from minus 50 volts to plus 50 volts,the numerical values of potentials being given consistent with suchrange of operation. 1

The potentials to 'be multiplied are E and E applied to the respectiveterminals 162 and 164. These terminals are connected to an array ofresistors 166, 168, 170, 172, 174, 176 and 178. The junction ofresistors 176 and 178 is connected to a terminal 182 to which there isapplied 150 volts. Alimited range multiplier, i.e., one which willoperate only on positive input potentials, is indicated at 186 and maybe of any of the types previously described or other conventional types.Its inputs are provided, respectively, from the junction of resistors170 and 176 and from the juncti gp of resistors 174 and 178. Its outputis delivered at 18% the series arrangement of resistors 190 and 192running to ground. A high gain differential amplifier has one inputprovided from the junction of resistors 190. and 192, and its otherinput from the terminal 184 at the junction of resistors 166 and 168.The output ofthe difierential amplifier is to a terminal 196 and to theseries arrangement of resistors 198 and 200 running to ground. Thejunction of these last resistors is connected to the same input as theterminal 184.

It will be noted that certain of the resistors mentioned have the samevalue R, while resistor 192 has a value 2R, resistor 1 98 has a valuethree-hal es R and resistor 200 has a value 3R. Resistors 170, 176, 178and 174 have equal values R which need not be related to R.

By following the voltage legends at the various terminals andconnections, the operation of the circuit will be apparent. At terminals162 and 164 the applied potentials E and E may vary both positively andnegatively. Through the introduction of the positive 150 volt potentialat terminal 182, the inputs to the multiplier are made essentiallypositive. The output of the multiplier is also essentially positive. Thehigh gain ditferential amplifier receives only positive potentials, but,since it operates between a high positive potential and a high negativepotential, its output may be either positive or negative within thelimits of operation. It will be noted that a scale factor of 100 isintroduced in the value of the output potential E so that thedifierential amplifier output varies within reasonable limits eventhough both of the inputs may be volts.

What is claimed is:

1. Apparatus of the type described comprising a pair of terminalsconnected respectively to potential sources, a first pair of diodesconnected in series between said terminals with their correspondingelectrodes connected to said terminals and their other electrodesconnected to a junction, a source of potential connected to saidjunctionto render said diodes normally conducting, a pair of. timeconstant resistance-capacitance circuits, a second pair of diodesrespectively connecting said time constant circuits to said terminals,said diodes of the second pair being disposed so as to be cut oil whenthe diodes of the first pair are conducting and to be conducting whenthe diodes'of the first pair are out 01f, whereby, during the lastmentioned condition said time constant circuits may be changed throughthe last mentioned diodes from the respective terminals, meansestablishing a fourth potential source, means responsive to substantialequality of said fourth potential and the potential of one of said timeconstant circuits to provide to said junction a potential to cut off thefirst mentioned diodes, and means for sampling the potential of theother of said time constant circuits at the time of cut ofi of the firstmentioned diodes.

References Cited in the file of this patent UNITED STATES PATENTS HirschSept. '15, 1953 OTHER REFERENCES Proceedings of the IRE (Broomall etal.), May 1952, pages 568572.

Trans. of the IRE, Prof. Group on Electronic Computers (Freeman et a1.),March 1954, pages 11-17.

